Families of similar birth and death processes in random environments

General repairable spare parts demand model based on quasi-birth-death process

General quasi-birth-death process model of repairable spare parts demand

Basic concept and existence of birth and death process in random environment

Basic concept and existence of birth and death process in random environment

Stationarity of birth and death process of double immigrants in random environment

Limit properties of birth and death process of double immigrants in random environment

Some ergodic criteria for general continuous-time quasi-birth-death processes and their applications

Ergodic criteria for general continuous-time quasi-birth-death processes and their applications

Now, we have solved the characteristic number of birth and death process with zero as the obstacle and its probability significance.

So far, this paper has solved the characteristic number and its probability significance of the birth and death process with 0 as two walls.

Finally, we apply the above results to the birth and death process, and get the digital description of the above conditions.

The necessary and sufficient condition for Iw to generate positive contractive semigroups on C is that there is a person 0, then? q； ; It is injective on ll

Markov chain: discrete-time Markov chain, state classification, ergodicity, stationary distribution. Continuous time Markov chain, birth and death process

Markov chain: discrete-time Markov chain, classification, ergodicity and stationary distribution of states. Continuous time Markov chain, birth and death process.

The characteristic number of birth and death process and its probability meaning have been solved by Professor Yang in [1] and Professor Wang in [2].

In Professor Yang's document [1] and Professor Wang Zikun's document [2], the characteristic number of birth and death process with 0 as the reflecting wall and its probability significance are solved.

The sixth chapter is the convergence rate of graduate extinction process. For the conservative birth-death q-matrix, we prove that the minimal q-function is strongly ergodic if and only if r-and S < Suppose a birth and death q matrix satisfies r < and s <

In chapter 6, the convergence rate in the process of birth and death is studied. The necessary and sufficient conditions for the strong ergodicity of conservative birth and death q- matrices are r = and s; When R and S exist, the unique true Q function is strongly ergodic.

In this thesis, the multi-channel sharing system is regarded as a random service system. Based on the steady-state solution of birth and death process with finite state space, the m/m/n/n/m queuing model, call blocking rate formula and channel utilization formula suitable for limited user systems are derived. With the help of the visual data analysis function of matlab software, the numerical divergence of each formula and the corresponding numerical divergence suitable for infinite user system are compared.

This paper regards the multi-channel communication system as a random service system. According to the steady-state solution of the finite state birth and death process, the formulas of call loss rate and channel utilization rate of multi-channel communication systems with unlimited users and limited users are derived by using two queuing models. With the help of the visual data analysis function of matlab, the numerical differences between the two groups of formulas are compared. The applicable conditions of two groups of formulas are pointed out.

The characteristic number and its probability meaning of the birth and death process of jumping reflection wall with zero as the standard have been partially solved by Professor Yang in [1], which depends on establishing a method to solve the pner equations with O boundary. On the basis of the former method, this paper establishes another method to solve the pner equations with one boundary, and further improves the characteristic number of the birth and death process of the zero-based jumping reflection wall and its probability significance.

In the document [1], Professor Yang created a method to understand the linear equations with two boundaries, and used this method to partially solve the characteristic number and its probability significance of the birth and death process of the flying wall with zero as the standard. Based on this method, this paper creates a method to understand the linear equations with boundary, and further improves the characteristic number and its probability significance of the birth and death process with 0 as the reflecting wall and quasi-flying wall by using these two methods.

In this paper, the theory and method of linear operator semigroup in functional analysis are used to prove the well-posedness of the solution of kolmogorov backward differential equation in birth and death process theory. The existence of upper eigenvalue of equation coefficient matrix is studied by using positive operator and conjugate operator theory.

In this paper, we mainly study the well-posedness of the solution of André Andrey Kolmogorov's backward differential equation in the quenching process theory by using the linear operator c0 semigroup theory in functional analysis, and study the existence of the dominant eigenvalue of the equation coefficient matrix operator by using the theory of positive operator and * * * yoke operator and some conclusions.